{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VPSS56T2IKQXEJRB2XUKSZYWVM","short_pith_number":"pith:VPSS56T2","canonical_record":{"source":{"id":"1401.5415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T18:36:53Z","cross_cats_sorted":[],"title_canon_sha256":"141363cb106cbbb1064b6bde8e53874acb0dcf6a53e741b503810d97599b0d6f","abstract_canon_sha256":"98c5eb865fe188d77382944e7cd394c516e64e25a3c9d1670db8a0cfad17a74f"},"schema_version":"1.0"},"canonical_sha256":"abe52efa7a42a1722621d5e8a96716ab25fa14266c4bf458cf4ec15680c1913c","source":{"kind":"arxiv","id":"1401.5415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5415","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5415v1","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5415","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"VPSS56T2IKQX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VPSS56T2IKQXEJRB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VPSS56T2","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VPSS56T2IKQXEJRB2XUKSZYWVM","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T18:36:53Z","cross_cats_sorted":[],"title_canon_sha256":"141363cb106cbbb1064b6bde8e53874acb0dcf6a53e741b503810d97599b0d6f","abstract_canon_sha256":"98c5eb865fe188d77382944e7cd394c516e64e25a3c9d1670db8a0cfad17a74f"},"schema_version":"1.0"},"canonical_sha256":"abe52efa7a42a1722621d5e8a96716ab25fa14266c4bf458cf4ec15680c1913c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:33.877930Z","signature_b64":"N1sjpmG4EZMTQpoRRw66VFn2I6nvyLGM/GoTd2WlQusFFrKUXKNFjWIw6QRhh17xd69QTaxV4v/JGD2SMmK3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe52efa7a42a1722621d5e8a96716ab25fa14266c4bf458cf4ec15680c1913c","last_reissued_at":"2026-05-18T03:01:33.877152Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:33.877152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5415","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9N/CK2cISO6rtTMIdh1UAqANIPNyzDYc0WQ0PGPP9KJGdFZ5MBj0HpvaBKrg7JDyas7Qf6j2xhHaNUAXW/dCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:15:12.198585Z"},"content_sha256":"89ff4b197abefcc66e0fabd27a7f56fd8d040e95957a08a4f6788a8d9880aa9c","schema_version":"1.0","event_id":"sha256:89ff4b197abefcc66e0fabd27a7f56fd8d040e95957a08a4f6788a8d9880aa9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VPSS56T2IKQXEJRB2XUKSZYWVM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on isotropic geometry of production models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bang-Yen Chen, Leopold Verstraelen, Simona Decu","submitted_at":"2014-01-21T18:36:53Z","abstract_excerpt":"The production function is one of the key concepts of mainstream neoclassical theories in economics. The study of the shape and properties of the production possibility frontier is a subject of great interest in economic analysis. In this respect, Cobb-Douglas and CES production functions with flat graph hypersurfaces in Euclidean spaces are first studied in [19,20]. Later, more general studies of production models were given in [4-10, 12, 21]. On the other hand, from visual-physical experiences, the second and third authors proposed in [14] to study production models via isotropic geometry. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5415","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yilZ/KMAMK/LR80603gENAB6NFwNbuAWWZXCz6VPqhA3rcE9xTQrJUIlgKuXj+Bd9yZ9NJL/cjDZ8iXscedUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T11:15:12.198929Z"},"content_sha256":"f4d83a97bc3bd675662007262a6b30b85c8821828e3d6526b2b627afbfcf56cf","schema_version":"1.0","event_id":"sha256:f4d83a97bc3bd675662007262a6b30b85c8821828e3d6526b2b627afbfcf56cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/bundle.json","state_url":"https://pith.science/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T11:15:12Z","links":{"resolver":"https://pith.science/pith/VPSS56T2IKQXEJRB2XUKSZYWVM","bundle":"https://pith.science/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/bundle.json","state":"https://pith.science/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPSS56T2IKQXEJRB2XUKSZYWVM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VPSS56T2IKQXEJRB2XUKSZYWVM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"98c5eb865fe188d77382944e7cd394c516e64e25a3c9d1670db8a0cfad17a74f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T18:36:53Z","title_canon_sha256":"141363cb106cbbb1064b6bde8e53874acb0dcf6a53e741b503810d97599b0d6f"},"schema_version":"1.0","source":{"id":"1401.5415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5415","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5415v1","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5415","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"VPSS56T2IKQX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VPSS56T2IKQXEJRB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VPSS56T2","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:f4d83a97bc3bd675662007262a6b30b85c8821828e3d6526b2b627afbfcf56cf","target":"graph","created_at":"2026-05-18T03:01:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The production function is one of the key concepts of mainstream neoclassical theories in economics. The study of the shape and properties of the production possibility frontier is a subject of great interest in economic analysis. In this respect, Cobb-Douglas and CES production functions with flat graph hypersurfaces in Euclidean spaces are first studied in [19,20]. Later, more general studies of production models were given in [4-10, 12, 21]. On the other hand, from visual-physical experiences, the second and third authors proposed in [14] to study production models via isotropic geometry. T","authors_text":"Bang-Yen Chen, Leopold Verstraelen, Simona Decu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T18:36:53Z","title":"Notes on isotropic geometry of production models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5415","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:89ff4b197abefcc66e0fabd27a7f56fd8d040e95957a08a4f6788a8d9880aa9c","target":"record","created_at":"2026-05-18T03:01:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"98c5eb865fe188d77382944e7cd394c516e64e25a3c9d1670db8a0cfad17a74f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-01-21T18:36:53Z","title_canon_sha256":"141363cb106cbbb1064b6bde8e53874acb0dcf6a53e741b503810d97599b0d6f"},"schema_version":"1.0","source":{"id":"1401.5415","kind":"arxiv","version":1}},"canonical_sha256":"abe52efa7a42a1722621d5e8a96716ab25fa14266c4bf458cf4ec15680c1913c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe52efa7a42a1722621d5e8a96716ab25fa14266c4bf458cf4ec15680c1913c","first_computed_at":"2026-05-18T03:01:33.877152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:33.877152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N1sjpmG4EZMTQpoRRw66VFn2I6nvyLGM/GoTd2WlQusFFrKUXKNFjWIw6QRhh17xd69QTaxV4v/JGD2SMmK3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:33.877930Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89ff4b197abefcc66e0fabd27a7f56fd8d040e95957a08a4f6788a8d9880aa9c","sha256:f4d83a97bc3bd675662007262a6b30b85c8821828e3d6526b2b627afbfcf56cf"],"state_sha256":"83df78fb1c7404e780d65ee337b777d55710ec9a6c633e3ef1982067a8283b2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NeUNT0B/PKJQOqn1mtY0xBXRgJEKrIk0Xp3nxTAMf463WpOpDswSHtoLCZ8A1YgZ9WWRyHCPZEPcTUN2GyGRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T11:15:12.200860Z","bundle_sha256":"ab9235b03f5c865adf81154eb27a88e956f032d25c7d613a6b65b6011b3ee6dd"}}